in the sense of Definition REF ,
we obtain the standard setting
of the (\(\mathbb {R}\) -valued) reproducing
kernel Hilbert space (RKHS; [1]}).
The kernel \(k\)  satisfies \(k(x,x^{\prime }) = k(x^{\prime },x)\) 
for all \(x,x^{\prime } \in E\) .
We obtain a space \({{H}}\)  consisting of functions
from \(E\)  to \(\mathbb {R}\) 
with the properties
